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From Calculus to Analysis / by Rinaldo B. Schinazi
版 | 1st ed. 2012. |
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出版者 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser |
出版年 | 2012 |
本文言語 | 英語 |
大きさ | X, 250 p. 7 illus : online resource |
著者標目 | *Schinazi, Rinaldo B author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Sequences (Mathematics) LCSH:Approximation theory LCSH:Measure theory FREE:Analysis FREE:Sequences, Series, Summability FREE:Approximations and Expansions FREE:Measure and Integration |
一般注記 | Preface -- Ch. 1 Number Systems -- 1.1 The algebra of the reals -- 1.2 Natural numbers and integers -- .1.3 Rational numbers and real numbers -- 1.4 Power functions -- Ch. 2 Sequences and Series -- 2.1 Sequences -- 2.2 Montone sequences, Bolzano-Weirestrass theorem and operations on limits -- 2.3 Series -- 2.4 Absolute convergence -- Ch. 3 Power series and special functions.-3.1 Power series.-3.2 Tigonometric functions -- 3.3 Inverse trigonometric functions -- 3.4 Exponential and logarithmic functions -- Ch 4 Fifty Ways to Estimate the Number pi.-4.1 Power series expansions -- 4.2 Wallis' integrals, Euler's formula, and Stirling's formula.-4.3 Convergence of infinite products -- 4.4 The number pi is irrational -- Ch. 5 Continuity, Limits, and Differentiation -- 5.1 Continuity -- 5.2 Limits of functions and derivatives -- 5.3 Algebra of derivatives and mean value theorems -- 5.4 Intervals, continuity, and inverse functions -- Ch. 6 Riemann Integration -- 6.1 Construction of the integral -- 6.2 Properties of the integral -- 6.3 Uniform continuity -- Ch 7 Decimal Represenation of Numbers -- Ch 8 Countable and Uncountable Sets -- Further Readings -- Index This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. Key features: * Contains numerous exercises; * Provides unique examples, such as many ways to estimate the number Pi; * Introduces the basic principles of analysis; * Offers a straightforward introduction to the calculus basics such as number systems, sequences, and series; * Carefully written book with a thoughtful perspective for students. From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will findthis text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course HTTP:URL=https://doi.org/10.1007/978-0-8176-8289-7 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9780817682897 |
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電子リソース |
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EB00236370 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000118780 |
ISBN | 9780817682897 |
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